Please help. what is the quotient of 4m^12/x-1÷x^2/8m^3 assume x ≠ 0 and m≠0
1 answer:
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A number line consists only of one axis, conventionally a horizontal axis. Just create a line, and scale it according to practicality and your preference. Usually, it has an interval of 1 unit. But for this case, since it is in fraction form, the interval should be smaller so that you can see clearly where it is located.
In decimal form, 13/17 is equal to 0.7647058824. Let's just round this off to 0.764, that can suffice already. So, you would expect it to be between 0.7 and 0.8 on the number line. Just estimate visually where it is located. Since, it is more than 0.75, the dot would be just slightly closer to 0.8 than 0.7. The exact location is shown in the attached picture.
In decimal form, 13/17 is equal to 0.7647058824. Let's just round this off to 0.764, that can suffice already. So, you would expect it to be between 0.7 and 0.8 on the number line. Just estimate visually where it is located. Since, it is more than 0.75, the dot would be just slightly closer to 0.8 than 0.7. The exact location is shown in the attached picture.
Step-by-step explanation:
The quadratic formula is honestly the most straightforward way of solving here.
Your other options are completing the square (which is the same thing as the quadratic formula but it's good to know that method if you have to take Integral Calculus at some point) or maybe factoring by grouping if it's appropriate. But the quadratic formula will work for you in all three equations:
1) a=1, b=0, c=8
This reduces pretty quickly into x=8i,-8i due to the negative under the radical. (Actually we didn't even really need the formula here.)
2) a=-9, b=4, c=-10
This reduces into x=(-4+i√(344))/-18, (-4-i√(344))/-18 and doesn't go any further because 344 isn't a perfect square.
3) a=1, b=8, c=17
This reduces to x=(-4+i), (-4-i)
So those are the answers for each.